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Quartic oscillator

  • Section VII
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Book cover Feynman Path Integrals

Part of the book series: Lecture Notes in Physics ((LNP,volume 106))

Abstract

On the example of the semi-classical expansion for the levels of the quartic oscillator −(d2/dq2) +q 4 , we show how the complex WKB method provides information about the singularities of the Borel transform of the semi-classical series. In this problem there occurs a tunneling effect between complex turning points, by which those singularities generate exponentially small, yet detectable, corrections to the energy levels.

Dedicated to the centennial of the instanton 1

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Author information

Authors and Affiliations

  1. Service de Physique Theorique, CEA-Saclay, BP no2, 91190, Gif-sur-Yvette, France

    R. Balian

  2. I.N.F.N., Frascati, Italy

    G. Parisi

  3. Service de Physique Théorique, CEA-Saclay, BP no2, 91190, Gif-sur-Yvette, France

    A. Voros (Member of CNRS)

Authors
  1. R. Balian
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  2. G. Parisi
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  3. A. Voros
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Editor information

S. Albeverio Ph. Combe R. Høegh-Krohn G. Rideau M. Sirugue-Collin M. Sirugue R. Stora

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© 1979 Springer-Verlag

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Balian, R., Parisi, G., Voros, A. (1979). Quartic oscillator. In: Albeverio, S., et al. Feynman Path Integrals. Lecture Notes in Physics, vol 106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09532-2_85

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  • DOI: https://doi.org/10.1007/3-540-09532-2_85

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  • Print ISBN: 978-3-540-09532-3

  • Online ISBN: 978-3-540-35039-2

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